EP1046885A1 - Method of calibrating pressure and temperature transducers - Google Patents
Method of calibrating pressure and temperature transducers Download PDFInfo
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- EP1046885A1 EP1046885A1 EP20000302899 EP00302899A EP1046885A1 EP 1046885 A1 EP1046885 A1 EP 1046885A1 EP 20000302899 EP20000302899 EP 20000302899 EP 00302899 A EP00302899 A EP 00302899A EP 1046885 A1 EP1046885 A1 EP 1046885A1
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01D—MEASURING NOT SPECIALLY ADAPTED FOR A SPECIFIC VARIABLE; ARRANGEMENTS FOR MEASURING TWO OR MORE VARIABLES NOT COVERED IN A SINGLE OTHER SUBCLASS; TARIFF METERING APPARATUS; MEASURING OR TESTING NOT OTHERWISE PROVIDED FOR
- G01D18/00—Testing or calibrating apparatus or arrangements provided for in groups G01D1/00 - G01D15/00
- G01D18/008—Testing or calibrating apparatus or arrangements provided for in groups G01D1/00 - G01D15/00 with calibration coefficients stored in memory
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01D—MEASURING NOT SPECIALLY ADAPTED FOR A SPECIFIC VARIABLE; ARRANGEMENTS FOR MEASURING TWO OR MORE VARIABLES NOT COVERED IN A SINGLE OTHER SUBCLASS; TARIFF METERING APPARATUS; MEASURING OR TESTING NOT OTHERWISE PROVIDED FOR
- G01D18/00—Testing or calibrating apparatus or arrangements provided for in groups G01D1/00 - G01D15/00
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01D—MEASURING NOT SPECIALLY ADAPTED FOR A SPECIFIC VARIABLE; ARRANGEMENTS FOR MEASURING TWO OR MORE VARIABLES NOT COVERED IN A SINGLE OTHER SUBCLASS; TARIFF METERING APPARATUS; MEASURING OR TESTING NOT OTHERWISE PROVIDED FOR
- G01D3/00—Indicating or recording apparatus with provision for the special purposes referred to in the subgroups
- G01D3/02—Indicating or recording apparatus with provision for the special purposes referred to in the subgroups with provision for altering or correcting the law of variation
- G01D3/022—Indicating or recording apparatus with provision for the special purposes referred to in the subgroups with provision for altering or correcting the law of variation having an ideal characteristic, map or correction data stored in a digital memory
Definitions
- quartz piezoelectric temperature transducers may be affected by pressure applied thereto.
- the accuracy of the acquired temperature data is affected.
- the temperature data is commonly used to correct the pressure data acquired by the pressure transducer. Nevertheless, it may be seen that the inaccuracies are compounded by using inaccurate temperature data to correct inaccurate pressure data.
- a method of calibrating a subject sensor in which the subject sensor generates an output indicative of a first stimulus, but the output is influenced at least transiently by a rate of change of a second stimulus.
- a second sensor is utilized in the method, the sensor generating an output indicative of the second stimulus.
- the subject and second sensors are subjected to known levels of the first and second stimuli at known discrete time intervals, and the outputs of the sensors at these stimulus levels are recorded.
- the subject and second sensor outputs, and the time intervals are then input to a neural network and the neural network is trained to generate an output which is a known mathematical function of the first stimulus in response to input to the neural network of outputs of the subject and second sensors at associated time intervals.
- the method further comprises the steps of: applying the series of second stimulus levels to a reference sensor; and generating an output of the reference sensor, the reference sensor output including a series of reference measurements of corresponding respective ones of the series of second stimulus levels, and wherein the inputting step further comprises inputting the reference sensor output to the neural network.
- the changes over time in the series of first stimulus levels are input to the neural network by associating each one of the series of first stimulus levels with a corresponding respective one of a series of relative time measurements generated by a clock device.
- each first calibrated measurement in the neural network output is generated in response to the corresponding respective first uncalibrated measurement in the first sensor output and a first predetermined quantity of prior first uncalibrated measurements.
- the neural network output portion is input via a tapped delay line.
- the first sensor and neural network are interconnected in a transducer.
- the method 66 also accomplishes calibration of a second subject sensor 70 which may also be incorporated into the transducer 12 of the method 10, or which may be utilized in other methods, other transducers, other applications, etc.
- the sensor 70 is described herein as being a temperature sensor, i.e., a sensor which produces an output indicative of temperature applied thereto.
- the subject sensor 70 may be any type of sensor and may produce an output indicative of stimuli other than temperature in keeping with the principles of the present invention.
- the pressure and/or temperature reference sensors 74, 80 are unnecessary and the pressure input 78 and temperature input 84 may be substituted for the reference sensor outputs 76, 82, respectively, in the further description of the method 66 below.
- the subject sensors 100, 102 it is not necessary, in keeping with the principles of the present invention, for the subject sensors 100, 102 to be in close proximity to each other, for the subject sensors to be included in the same transducer, or for the subject sensors to be pressure and temperature sensors.
- a clock 158 is provided in the method 130, so that the relative time at which each of the pressures (P1, P2, ..., Pn) and/or temperatures (T1, T2, ..., Tn) is/are applied to the subject pressure and/or temperature sensors 132, 134 may be determined.
- the clock 158 produces an output 160 indicative of the time at which corresponding respective pressures and/or temperatures are applied in the inputs 136, 150.
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Abstract
Description
- The present invention relates generally to a method and apparatus utilized to calibrate sensors, and more particularly relates to a method and apparatus for calibrating pressure and temperature transducers utilized in tools in subterranean wells.
- It is common practice to use transducers in downhole tools for various purposes. For example, in a drill stem test or other well test, important information regarding the present and future productivity of a well may be determined by evaluating pressure, temperature, flow rate, etc. data recorded during the test. Unfortunately, the accuracy of that information is necessarily dependent upon the accuracy of the recorded data from which it is derived.
- Typically, the pressure, temperature, flow rate, etc. data is acquired from outputs of transducers or other sensor apparatus positioned downhole during the test. In this manner, the sensors are positioned in relatively close proximity to a particular formation or zone being evaluated in the test, thereby minimizing the contribution of wellbore storage effects, resistance to flow, temperature changes, etc. to the collected data. However, such downhole positioning of the sensors creates other problems which affect the accuracy of the sensor outputs.
- Quartz piezoelectric pressure transducers are generally used in well tests, due to their superior accuracy as compared to other types of commercially available pressure transducers. When a conventional quartz pressure transducer is positioned downhole, however, it is subjected to whatever static or dynamic temperature conditions exist in the downhole environment. Since the output of a conventional quartz pressure transducer is affected by the temperature of the piezoelectric sensor therein, the precise manner in which the transducer output is affected by temperature must be known, and the output of the transducer must be appropriately corrected for the temperature at which the output data was taken, in order to increase the accuracy of the data.
- In a similar manner, quartz piezoelectric temperature transducers may be affected by pressure applied thereto. Thus, if a quartz temperature transducer is subjected to pressures existing downhole during a well test, the accuracy of the acquired temperature data is affected. Fortunately, such inaccuracies in the temperature data are generally considered to be relatively minor, and so the temperature data is commonly used to correct the pressure data acquired by the pressure transducer. Nevertheless, it may be seen that the inaccuracies are compounded by using inaccurate temperature data to correct inaccurate pressure data.
- Again, in a similar manner, flow rate data collected from the output of a flow rate sensor is typically affected by conditions existing downhole. For example, since the output of a common flow rate sensor is typically influenced by the temperature of the fluid for which the flow rate is being sensed, the flow rate sensor output data must be corrected for the temperature of the fluid at the time the output is generated. Such influence of fluid temperature on flow rate sensor output usually affects the accuracy of the acquired data greatest when the fluid is a gas, or a liquid with gas entrained therein.
- Sensors used in downhole environments may be affected by other factors as well. For example, the output of a quartz piezoelectric pressure sensor is not only affected by the temperature of the surrounding environment, it is also affected by changes in the temperature of the surrounding environment, such as the rate of temperature change. This is due to the fact that the pressure sensor is sensitive to stresses in a quartz crystal thereof and stresses are induced in the quartz crystal in response to changes in the temperature of the crystal.
- In the past, a quartz pressure transducer was statically calibrated by placing the transducer in a fluid bath at a known constant temperature and recording the output of the transducer at various pressures applied thereto. In this manner, a sensor output profile at that temperature was obtained. This procedure was then repeated at different temperatures, with a sensor output profile being generated for each temperature. Thus, a set of sensor output profiles was generated, each profile corresponding to a different temperature.
- When the output of a particular pressure transducer was evaluated in actual practice, for example, after a well test, the output would be corrected based on the temperature of the surrounding environment at the time the output data was acquired. However, since the temperature of the surrounding environment typically fell between two of the temperatures used in the procedure to generate the sensor output profiles, it was generally necessary to interpolate between the corresponding sensor output profiles. Such interpolation usually assumed that a linear relationship existed between the output profiles and the corresponding temperatures at which they were generated and, since this linear relationship is generally not the case, this introduced further inaccuracies into the resulting corrected output data. Additionally, this method did not compensate at all for changes in temperature at the time the sensor output data was acquired.
- Therefore, from the foregoing, it is apparent that a need exists for improved methods of calibrating sensors and, in particular, a need exists for utilizing such improved methods for calibrating sensors used in downhole environments. Furthermore, it would be desirable to provide such methods which compensate for changes in the environments in which the sensors are operated.
- In carrying out the principles of the present invention, in accordance with described embodiments thereof, methods are provided which enable sensors to be calibrated with enhanced accuracy. The methods may be particularly useful for sensors utilized in applications where environmental conditions change during use of the sensors, such as in downhole transducer applications. Associated apparatus are also provided.
- In one aspect of the present invention, a subject sensor which generates an output indicative of a stimulus is subjected to multiple levels of the stimulus. For example, a pressure sensor may be subjected to multiple fluid pressure levels. The output of the subject sensor is determined at each of the stimulus levels. A known accurate reference sensor is also subjected to the multiple stimulus levels and its output determined at each of the stimulus levels. The output of the subject sensor for the applied stimulus levels is then input to a neural network. The neural network is trained so that, when an output of the subject sensor is input to the neural network, the neural network simulates an output of the reference sensor.
- In this manner, an output of the known accurate reference sensor is simulated in response to an input to the neural network of an output of the subject sensor. This method may be particularly useful in applications where the subject sensor is exposed only to changes in the stimulus level, or where the output of the subject sensor is not influenced by other stimulus levels. For example, where the subject sensor is a pressure sensor either not exposed to, or unaffected by, changes in temperature.
- In another aspect of the present invention, the neural network has input to it multiple levels of a second stimulus which affects the output of the subject sensor. For example, where the subject sensor is a pressure sensor, the output of which is influenced by the temperature of the sensor. During training of the neural network, known levels of the second stimulus, such as in the form of output of a second known accurate reference sensor, at each of the outputs of the subject sensor are input to the neural network. Thereafter, the calibrated neural network output will compensate for the influence of the second stimulus level in simulating an output of the known accurate reference sensor in response to an input to the neural network of an output of the subject sensor and the second stimulus level.
- In still another aspect of the present invention, a method of calibrating a subject sensor is provided in which outputs of both the subject sensor and a second sensor are input to a neural network. In this case, the subject sensor generates an output indicative of a first stimulus and the second sensor generates an output indicative of a second stimulus. The output of the subject sensor in response to each of multiple levels of the first stimulus is determined, with the subject sensor also being subjected to one of multiple levels of the second stimulus at each of the first stimulus levels. The output of the second sensor is determined in response to the level of the second stimulus at each of the first stimulus levels. A first known accurate reference sensor is also subjected to the first stimulus levels and its output determined at each of these. A second known accurate reference sensor is also subjected to the second stimulus levels and its output determined at each of these. The subject sensor outputs and the second sensor outputs are then input to a neural network and, using this data, the neural network is trained to simulate outputs of the reference sensors in response to input to the neural network of outputs of the subject and second sensors.
- In this manner, an output of the first reference sensor is simulated in response to input to the neural network of outputs of the subject and second sensors. This method may be particularly useful in applications in which the subject sensor output is influenced by the stimulus indicated by the second sensor. For example, in applications where the subject sensor is a pressure sensor whose output is influenced by temperature, which property is indicated by the second sensor.
- In yet another aspect of the present invention, a method of calibrating a subject sensor is provided in which the subject sensor generates an output indicative of a first stimulus, but the output is influenced at least transiently by a rate of change of a second stimulus. A second sensor is utilized in the method, the sensor generating an output indicative of the second stimulus. The subject and second sensors are subjected to known levels of the first and second stimuli at known discrete time intervals, and the outputs of the sensors at these stimulus levels are recorded. The subject and second sensor outputs, and the time intervals are then input to a neural network and the neural network is trained to generate an output which is a known mathematical function of the first stimulus in response to input to the neural network of outputs of the subject and second sensors at associated time intervals.
- In this manner, a subject sensor, which has an output indicative of a first stimulus, but influenced at least in part by changes in a second stimulus, may be calibrated using a second sensor which has an output indicative of the second stimulus, with the outputs of the subject and second sensors being taken at known time intervals. This method may, for example, be useful where the subject sensor is a pressure sensor whose output is influenced by a rate of change in temperature of the surrounding environment.
- According to another aspect of the invention there is provided a calibration method, comprising the steps of: applying an input to a first subject sensor, the first subject sensor input including a series of levels of a first stimulus; generating an output of the first subject sensor in response to the first subject sensor input, the first subject sensor output including a series of uncalibrated measurements of corresponding respective ones of the series of first stimulus levels; inputting the first subject sensor output to a neural network; and training the neural network to generate a calibrated output of the first subject sensor.
- In an embodiment, the training step further comprises adjusting the neural network to generate the calibrated first subject sensor output including a series of calibrated measurements which are related to corresponding respective ones of the series of first stimulus levels by a known mathematical function.
- In an embodiment, the training step further comprises adjusting the neural network to generate the calibrated first subject sensor output including a series of calibrated measurements which are related by a known mathematical function to corresponding respective ones of a series of reference measurements of corresponding respective ones of the series of first stimulus levels generated by a reference sensor.
- In an embodiment, in the applying step, the first subject sensor input further includes a series of levels of a second stimulus, and wherein in the generating step, the series of first subject sensor output uncalibrated measurements are influenced at least in part by corresponding respective ones of the series of second stimulus levels.
- In an embodiment, the inputting step further comprises inputting the series of second stimulus levels to the neural network.
- In an embodiment, the method further comprises the steps of: applying the series of second stimulus levels to a reference sensor; and generating an output of the reference sensor, the reference sensor output including a series of reference measurements of corresponding respective ones of the series of second stimulus levels, and wherein the inputting step further comprises inputting the reference sensor output to the neural network.
- In an embodiment, the method further comprises the steps of: applying an input to a second subject sensor, the second subject sensor input including a series of levels of a second stimulus; generating an output of the second subject sensor in response to the second subject sensor input, the second subject sensor output including a series of uncalibrated measurements of corresponding respective ones of the series of second stimulus levels; and inputting the second subject sensor output to the neural network, and wherein the training step further comprises training the neural network to generate a calibrated output of the second subject sensor.
- In an embodiment, the training step further comprises adjusting the neural network to generate the calibrated first subject sensor output including a series of calibrated measurements which are related to corresponding respective ones of the first stimulus levels by a known mathematical function.
- In an embodiment, the training step further comprises adjusting the neural network to generate the calibrated first subject sensor output including a series of calibrated measurements which are related to corresponding respective ones of a series of reference measurements of the series of first stimulus levels generated by a reference sensor, the calibrated measurements being related to the corresponding respective ones of the series of reference measurements by a known mathematical function.
- In an embodiment, the training step further comprises adjusting the neural network to generate the calibrated second subject sensor output including a series of calibrated measurements which are related to corresponding respective ones of the series of second stimulus levels by a known mathematical function.
- In an embodiment, the training step further comprises adjusting the neural network to generate the calibrated second subject sensor output including a series of calibrated measurements which are related to corresponding respective ones of a series of reference measurements of the series of second stimulus levels generated by a reference sensor, the calibrated measurements being related to the corresponding respective ones of the series of reference measurements by a known mathematical function.
- In an embodiment, in the first subject sensor input applying step, the first subject sensor input further includes the series of second stimulus levels, and wherein in the first subject sensor output generating step, the first subject sensor output is influenced at least in part by the series of second stimulus levels.
- In an embodiment, in the second subject sensor input applying step, the second subject sensor input further includes the series of first stimulus levels, and wherein in the second subject sensor output generating step, the second subject sensor output is influenced at least in part by the series of first stimulus levels.
- In an embodiment, the method further comprises the step of generating an output of a clock device, the output including a series of individual time indications, and wherein the inputting step further comprises inputting the clock device output to the neural network, with ones of the series of individual time indications being identified with corresponding respective ones of the series of first stimulus levels.
- In an embodiment, in the first subject sensor output generating step, the uncalibrated measurements of the series of first stimulus levels are influenced at least in part by changes over time in the first subject sensor input.
- In an embodiment, in the inputting step, the changes over time in the first subject sensor input are input to the neural network by associating each one of the series of uncalibrated measurements of the series of first stimulus levels with a corresponding respective one of a series of relative time measurements generated by a clock device.
- In an embodiment, in the training step, the neural network is trained to generate the calibrated output of the first subject sensor which compensates for the influence of the changes over time in the first subject sensor input on the series of uncalibrated measurements of the series of first stimulus levels.
- In an embodiment, in the first subject sensor output generating step, the uncalibrated measurements of the series of first stimulus levels are influenced at least in part by changes over time in a series of second stimulus levels.
- In an embodiment, in the inputting step, the changes over time in the series of second stimulus levels are input to the neural network by associating each one of the series of second stimulus levels with a corresponding respective one of a series of relative time measurements generated by a clock device.
- In an embodiment, in the training step, the neural network is trained to generate the calibrated output of the first subject sensor which compensates for the influence of the changes over time in the series of second stimulus levels on the uncalibrated measurements of the series of first stimulus levels.
- In an embodiment, the method further comprises the steps of applying an input to a second subject sensor, the second subject sensor input including the series of second stimulus levels; and generating an output of the second subject sensor in response to the second subject sensor input, the second subject sensor output including a series of uncalibrated measurements of corresponding respective ones of the series of second stimulus levels, and wherein the inputting step further comprises inputting the second subject sensor output to the neural network.
- In an embodiment, the training step further comprises training the neural network to generate a calibrated output of the second subject sensor.
- In an embodiment, in the second subject sensor output generating step, the series of uncalibrated measurements of the series of second stimulus levels is influenced at least in part by changes over time in the series of first stimulus levels.
- In an embodiment, in the inputting step, the changes over time in the series of first stimulus levels are input to the neural network by associating each one of the series of first stimulus levels with a corresponding respective one of a series of relative time measurements generated by a clock device.
- In an embodiment, in the training step, the neural network is trained to generate the calibrated output of the second subject sensor which compensates for the influence of the changes over time in the series of first stimulus levels on the uncalibrated measurements of the series of second stimulus levels.
- In an embodiment, in the training step, the neural network generates a first output including a series of measurements indicative of corresponding respective ones of the series of first stimulus levels.
- In an embodiment, in the training step, each of the series of measurements in the neural network first output is generated in response to input to the neural network of a selected predetermined quantity of the series of uncalibrated first stimulus level measurements in the first subject sensor output.
- In an embodiment, in the training step, the selected predetermined quantity of the series of uncalibrated first stimulus level measurements includes a predetermined quantity of the series of uncalibrated first stimulus level measurements generated prior to the uncalibrated first stimulus level measurement for which each of the series of measurements in the neural network first output is generated.
- In an embodiment, in the training step, the selected predetermined quantity of the series of uncalibrated first stimulus level measurements includes a first predetermined quantity of the series of uncalibrated first stimulus level measurements generated subsequent to the uncalibrated first stimulus level measurement for which each of the series of measurements in the neural network first output is generated.
- In an embodiment, in the training step, the selected predetermined quantity of the series of uncalibrated first stimulus level measurements further includes a second predetermined quantity of the series of uncalibrated first stimulus level measurements generated prior to the uncalibrated first stimulus level measurement for which each of the series of measurements in the neural network first output is generated.
- In an embodiment, in the training step, a series of a selected predetermined quantity of the series of measurements in the neural network first output generated prior to corresponding respective ones of each of the series of measurements in the neural network first output is input to the neural network.
- In an embodiment, in the training step, the series of the selected predetermined quantity of the series of measurements in the neural network first output is input to the neural network via a tapped delay line.
- According to another aspect of the invention there is provided a method of calibrating first and second sensors, the first sensor generating an output indicative of a first series of levels of a first stimulus applied to the first sensor and influenced by a change in a second series of levels of a second stimulus applied to the first and second sensors, and the second sensor generating an output indicative of the second series of levels of the second stimulus, the method comprising the steps of: time indexing the first and second sensor outputs; inputting the first and second sensor outputs to a neural network; and training the neural network by generating a first output of the neural network corresponding to the first sensor output, utilizing a first tapped delay line to input a first portion of the neural network first output to the neural network, generating a second output of the neural network corresponding to the second sensor output, and utilizing a second tapped delay line to input a second portion of the neural network second output to the neural network.
- In an embodiment, the first sensor output includes a series of first uncalibrated measurements corresponding to respective ones of the first series of the levels of the first stimulus, and in the training step, for each one of a series of first measurements included in the first neural network output corresponding to a respective one of the first series of uncalibrated measurements, a first predetermined quantity of the series of the first uncalibrated measurements prior to the respective one of the first series of uncalibrated measurements is input to the neural network.
- In an embodiment, in the training step, for each one of the series of first measurements included in the first neural network output corresponding to the respective one of the first series of uncalibrated measurements, a second predetermined quantity of the series of the first uncalibrated measurements subsequent to the respective one of the first series of uncalibrated measurements is input to the neural network.
- In an embodiment, the second sensor output includes a series of second uncalibrated measurements corresponding to respective ones of the second series of the levels of the second stimulus, and wherein in the training step, for each one of a series of measurements included in the second neural network output corresponding to a respective one of the second series of uncalibrated measurements, a third predetermined quantity of the series of the second uncalibrated measurements prior to the respective one of the second series of uncalibrated measurements is input to the neural network.
- In an embodiment, in the training step, for each one of the series of measurements included in the second neural network output corresponding to the respective one of the second series of uncalibrated measurements, a fourth predetermined quantity of the series of the second uncalibrated measurements prior to the respective one of the second series of uncalibrated measurements is input to the neural network.
- According to another aspect of the invention there is provided a method of calibrating a first sensor operatively positionable in a subterranean well, the method comprising the steps of: applying a first sensor input to the first sensor, the first sensor input including multiple levels of a first stimulus; generating a first output of the first sensor in response to the first sensor input; inputting the first sensor first output to a neural network; and training the neural network so that the neural network generates a first neural network output which is related to the first sensor input by a first known mathematical function.
- In an embodiment, the method further comprising the steps of: positioning the first sensor within the well; applying a second sensor input including multiple levels of the first stimulus to the first sensor within the well; generating a second output of the first sensor in response to the second sensor input; inputting the first sensor second output to the neural network; and generating a second output of the neural network which is related to the second sensor input by the first known mathematical function.
- In an embodiment, the positioning step further comprises including the first sensor in a transducer installed in the well.
- In an embodiment, the positioning step further comprises including the neural network in the transducer.
- In an embodiment, the positioning step further comprises remotely positioning the neural network relative to the first sensor.
- In an embodiment, the method further comprises the steps of: applying a second sensor input to a second sensor, the second sensor input including multiple levels of a second stimulus; and generating a first output of the second sensor in response to the second sensor input, and wherein the inputting step further comprises inputting the second sensor first output to the neural network, and wherein the training step further comprises training the neural network so that the neural network generates a second neural network output which is related to the second sensor input by a second known mathematical function.
- In an embodiment, the second sensor input applying step further comprises applying the second sensor input to the first sensor along with the first sensor input, and wherein in the first sensor first output generating step, the first sensor output is influenced at least in part by the second sensor input.
- In an embodiment, the training step further comprises training the neural network so that the first neural network output is compensated for the influence of the second sensor input on the first sensor first output.
- In an embodiment, in the first sensor first output generating step, the first sensor first output is influenced at least in part by a change over time of the second sensor input.
- In an embodiment, the training step further comprises training the neural network so that the first neural network output is compensated for the influence of the change over time of the second sensor input on the first sensor first output.
- In an embodiment, the training step further comprises utilizing at least one tapped delay line to input portions of the first neural network output to the neural network.
- According to another aspect of the invention there is provided apparatus operative in conjunction with a subterranean well, the apparatus comprising: a first sensor generating an output indicative of a series of first stimulus levels applied to the first sensor, the first sensor output including a series of first uncalibrated measurements of corresponding respective ones of the series of first stimulus levels; and a neural network generating an output in response to the first sensor output, the neural network output including a series of first calibrated measurements of corresponding respective ones of the series of first stimulus levels.
- In an embodiment, each of the series of first calibrated measurements is related by a known mathematical function to a corresponding respective one of the series of first stimulus levels.
- In an embodiment, the first sensor output is influenced at least in part by a series of second stimulus levels applied to the first sensor simultaneously with the series of first stimulus levels, and wherein the neural network output is generated further in response to the series of second stimulus levels.
- In an embodiment, the apparatus further comprises a clock device, the clock device time indexing each of the series of first uncalibrated measurements in the first sensor output.
- In an embodiment, the neural network output is compensated for changes in the first sensor output over time.
- In an embodiment, each first calibrated measurement in the neural network output is generated in response to the corresponding respective first uncalibrated measurement in the first sensor output and a first predetermined quantity of prior first uncalibrated measurements.
- In an embodiment, each first calibrated measurement in the neural network output is further generated in response to a second predetermined quantity of first uncalibrated measurements subsequent to the corresponding respective first uncalibrated measurement in the first sensor output.
- In an embodiment, each first calibrated measurement in the neural network output is generated in response to the corresponding respective first uncalibrated measurement in the first sensor output and a predetermined quantity of subsequent first uncalibrated measurements.
- In an embodiment, a portion of the neural network output is input to the neural network.
- In an embodiment, the neural network output portion is input via a tapped delay line.
- In an embodiment, the apparatus further comprises a second sensor generating an output indicative of a series of second stimulus levels applied to the second sensor, the second sensor output including a series of second measurements of corresponding respective ones of the series of second stimulus levels, the first sensor output being influenced at least in part by the series of second stimulus levels, and the neural network output being generated further in response to the second sensor output.
- In an embodiment, the neural network output further includes a series of second calibrated measurements of corresponding respective ones of the series of second stimulus levels.
- In an embodiment, the second measurements in the second sensor output are uncalibrated, and the neural network output further includes a series of second calibrated measurements of corresponding respective ones of the series of second stimulus levels.
- In an embodiment, the second sensor output is influenced at least in part by the series of first stimulus levels applied to the second sensor simultaneously with the series of second stimulus levels.
- In an embodiment, the apparatus further comprises a clock device, the clock device time indexing each of the series of first uncalibrated measurements in the first sensor output and each of the series of second measurements in the second sensor output.
- In an embodiment, the neural network output is compensated for changes in the second sensor output over time.
- In an embodiment, each second calibrated measurement in the neural network output is generated in response to the corresponding respective second measurement in the second sensor output and a first predetermined quantity of prior second measurements.
- In an embodiment, each second calibrated measurement in the neural network output is further generated in response to a second predetermined quantity of second measurements subsequent to the corresponding respective second measurement in the second sensor output.
- In an embodiment, each second calibrated measurement in the neural network output is generated in response to the corresponding respective second measurement in the second sensor output and a predetermined quantity of subsequent second measurements.
- In an embodiment, a portion of the neural network output is input to the neural network.
- In an embodiment, the neural network output portion is input via a tapped delay line.
- In an embodiment, the first sensor and neural network are interconnected in a transducer.
- In an embodiment, the transducer is positioned within the well.
- In an embodiment, the first sensor and the neural network are remotely located with respect to each other.
- Reference is now made to the accompanying drawings, in which:
- FIG. 1 is a schematic view of an embodiment of a well testing method according to the present invention;
- FIG. 2 is a schematic flow chart of a first embodiment of a method of calibrating sensors, according to the present invention;
- FIG. 3 is a schematic flow chart of a second embodiment of a method of calibrating sensors, according to the present invention;
- FIG. 4 is a schematic flow chart of a third embodiment of a method of calibrating sensors, according to the present invention;
- FIG. 5 is a schematic flow chart of a fourth embodiment of a method of calibrating sensors, according to the present invention;
- FIG. 6 is a schematic flow chart of a fifth embodiment of a method of calibrating sensors, according to the present invention;
- FIG. 7 is a schematic flow chart of a sixth embodiment of a method of calibrating sensors, according to the present invention;
- FIG. 8 is a representative chart of actual outputs of pressure and temperature sensors; and
- FIG. 9 is a representative chart of the pressure and temperature sensor outputs of FIG. 8 after using the calibration method of FIG. 7.
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- Representatively illustrated in FIG. 1 is a
method 10 which may embody principles of the present invention. In the following description of themethod 10 and other apparatus and methods described herein, directional terms, such as "above", "below", "upper", "lower", etc., are used for convenience in referring to the accompanying drawings. Additionally, it is to be understood that the various embodiments of the present invention described herein may be utilized in various orientations, such as inclined, inverted, horizontal, vertical, etc., without departing from the principles of the present invention. - The
method 10 is representatively illustrated in FIG. 1 as comprising a type of well test known as a drill stem test, wherein atransducer 12 is utilized to determine the temperature and pressure in close proximity to a formation or zone ofinterest 14 intersected by awellbore 16. However, it is to be clearly understood that principles of the present invention may be incorporated into many methods other than those described herein. For example, thewellbore 16 may be cased instead of open or uncased as depicted in FIG. 1, it is not necessary for methods incorporating principles of the present invention to comprise drill stem tests or other types of well tests, thetransducer 12 may be otherwise positioned, multiple transducers may be utilized, etc. Thus, it will be readily appreciated that the principles of the present invention are not limited to the specific embodiments of themethod 10 described herein. - In one type of conventional drill stem test, the
zone 14 is isolated from the remainder of the well, such as by setting one ormore packers 18 in thewellbore 16, the packer being conveyed into the wellbore as a part of atubular string 20. Thestring 20 also includes avalve 22 for selectively permitting and preventing fluid flow through the string. When thevalve 22 is opened, fluid (indicated by arrows 24) is permitted to flow into thestring 20 and, e.g., to the earth's surface. When thevalve 22 is closed, the fluid 24 is not permitted to flow through thestring 20, but is contained in the string below the valve and in thewellbore 16 below thepacker 18. - It is common practice in drill stem tests to perform tests known as drawdown and buildup tests when it is desired to evaluate the potential productivity of a zone, such as
zone 14. A transducer, such astransducer 12, is used to determine the pressure and temperature downhole during these tests. This data may then be evaluated prior to making important decisions, such as whether to expend the capital necessary to put the zone into production. Thus, the accuracy of the data procured during the tests may very well make the difference between making a correct decision and making an incorrect decision regarding thezone 14, or regarding the entire well. - In the
method 10, thetransducer 12 has been accurately calibrated using one of the calibration methods described more fully below. Such calibration ensures that the data procured by thetransducer 12 is more accurate than that available with previous methods, and gives those persons making decisions regarding thezone 14 and the remainder of the well increased confidence in the correctness of those decisions. - Referring additionally now to FIG. 2, a
method 26 of calibrating asensor 28 is schematically and representatively illustrated in flow chart form. Thesubject sensor 28 may be incorporated into thetransducer 12 of themethod 10, or it may be utilized in other methods, other transducers, other applications, etc., without departing from the principles of the present invention. Additionally, thesubject sensor 28 is described herein as being a pressure sensor, i.e., a sensor which produces an output indicative of pressure applied thereto. However, it is to be clearly understood that thesubject sensor 28 may be any type of sensor and may produce an output indicative of one or more stimuli other than pressure in keeping with the principles of the present invention. As used herein, the term "stimulus" is used to describe any stimulus which may be sensed or detected by a sensor, for example, temperature, pressure, pH, salinity, acceleration, speed, displacement, wavelength, fluid flow rate, density, weight, etc. - In the
method 26, areference sensor 30 is used in the initial calibration of thesubject sensor 28. In the illustrated situation in which thesubject sensor 28 is a pressure sensor, thereference sensor 30 is also a pressure sensor. Of course, if thesubject sensor 28 is a temperature sensor in actual practice, thereference sensor 30 would also be a temperature sensor. - The
reference sensor 30 generates anoutput 32 of known accuracy, that is, its output has a known mathematical relationship topressures 34 applied thereto, whether the output takes the form of a frequency, a voltage, a current, combinations thereof, other forms, etc. Thus, theoutput 32 of thereference sensor 30 is designated with the notation (act.), since it has a known relationship to theactual pressures 34 applied to the reference sensor. Of course, if theactual pressures 34 applied to thesubject sensor 28 can be known by other means, then use of thereference sensor 30 is unnecessary in themethod 26, and the knownactual pressures 34 may be substituted for thereference sensor output 32 referred to herein. - The
same pressures 34 applied to thereference sensor 30 are also applied to thesubject sensor 28, which generates anoutput 36 in response thereto. Preferably, but not necessarily, thepressures 34 are simultaneously applied to the subject andreference sensors output 36 of thesubject sensor 28 is designated with the notation (meas.), since it comprises the pressures as measured or determined by the subject sensor. - Note that the
input pressures 34 include multiple individual fluid pressures (P1, P2, ..., Pn), resulting in respective multiple individual pressure indications (P1(meas.), P2(meas.), ..., Pn(meas.)) in thesubject sensor output 36 and respective multiple individual pressure indications (P1(act.), P2(act.), ..., Pn(act.)) in thereference sensor output 32. Preferably, but not necessarily, theinput pressures 34 cover or span a range equal to or greater than the intended operating pressure range of thesubject sensor 28. - The
output 36 of thesubject sensor 28 is then input to aneural network 38 of the type well known to those skilled in the art. Theneural network 38 used in themethod 26 may be a multi-layer perceptron network, i.e., a network in which sums of individually weighted inputs are output to at least one activation function (e.g., log-sigmoid, symmetric saturating linear, linear, hard limit, etc.) within each layer. However, it is to be clearly understood that other types of neural networks may be utilized in themethod 26, without departing from the principles of the present invention. - Note that in the
method 26, theneural network 38 is a one input, one output network. Theneural network 38 is "trained" by inputting the individual pressure indications in thesubject sensor output 36 to the neural network, and comparing anoutput 40 of the neural network to the respective individual pressure indications in thereference sensor output 32, using procedures well known to those skilled in the art (e.g., by adjusting the values of the individual weights in the neural network). When theneural network output 40 simulates thereference sensor output 32 with an acceptable degree of accuracy (i.e., the neural network output bears a known mathematical relationship to thepressures 34 input to the subject andreference sensors 28, 30) in response to input thereto of thesubject sensor output 36, the neural network is trained. - When the
neural network 38 is trained, the known mathematical relationship may be applied to itsoutput 40, which was generated in response to theoutput 36 of thesubject sensor 28, in order to determine theactual pressures 34 applied to the subject sensor. Thus, theoutput 40 of theneural network 38 is designated with the notation (cal.), since it results from a calibration of thesubject sensor 28 produced by the neural network. Thereafter, when an unknown pressure is applied to thesubject sensor 28, and the output of the subject sensor is input to theneural network 38, the neural network will generate an output to which the known mathematical function may be applied to determine accurately the pressure applied to the subject sensor. Of course, the known mathematical function may be the identity function, in which case the neural network output will have values which correspond identically quantitatively to the respective values of the pressures applied to thesubject sensor 28, but this is not necessary in themethod 26. - The
neural network 38 may take any of a variety of forms when used in actual practice to calibrate, and thereafter produce calibrated outputs of, thesubject sensor 28. During the training process, theneural network 38 may exist virtually, such as when software is used to train a representation of the neural network on a computer. The trained virtualneural network 38 may then be utilized in actual practice by inputting output of thesubject sensor 28 to the computer (or another computing device into which the virtual neural network has been loaded or stored), the computer in response then generating a calibrated output. Alternatively, theneural network 38 may exist as an electronic circuit or may take another form, etc. - As described above, the
sensor 28 may be included in thetransducer 12. Theneural network 38 may also be included in thetransducer 12, so that the transducer thereby generates a calibrated output in response to pressure applied thereto, or the neural network may be positioned external to the transducer, such as in another portion of thestring 20 or at the earth's surface, so that the transducer output is calibrated after it leaves the transducer. Of course, it is not necessary for theneural network 38 to be directly connected to thesensor 28 ortransducer 12, since any data transmission means may be used to provide communication therebetween, and since the output of the sensor or transducer may be stored for later input to the neural network. For example, a data recording device, such as nonvolatile electronic memory, may be used to record the output of thetransducer 12 during the well test described above, and then retrieved later for analysis, including input of the recorded data to theneural network 38 to thereby generate a calibrated output of the transducer. - It will be readily appreciated that the
method 26 described above permits a sensor to be accurately calibrated with respect to pressures or other stimulus applied thereto. However, it is sometimes the case that more than one stimulus to which a sensor is exposed affects the output of the sensor. For example, a sensor may generate an output which is indicative of a first stimulus applied to the sensor, but the output is influenced, at least in part, by a second stimulus applied to the sensor. - Referring additionally now to FIG. 3, another
method 42 of calibrating asensor 44 is schematically and representatively illustrated in flow chart form. Thesubject sensor 44 may be incorporated into thetransducer 12 of themethod 10, or it may be utilized in other methods, other transducers, other applications, etc., without departing from the principles of the present invention. Additionally, thesubject sensor 44 is described herein as being a pressure sensor, i.e., a sensor which produces an output indicative of pressure applied thereto. However, it is to be clearly understood that thesubject sensor 44 may be any type of sensor and may produce an output indicative of stimuli other than pressure in keeping with the principles of the present invention. - The
subject sensor 44 generates an output which is indicative of pressure applied thereto, but this output is also influenced, at least in part, by temperature applied to the sensor. This is often the case with sensors which include quartz piezoelectric crystals, and which are frequently used in downhole applications, such as in the types of well tests described above. - In the
method 42, aninput 48 to thesubject sensor 44 includes both pressures and temperatures. Thus, for each pressure (P1, P2, ..., Pn) applied to thesubject sensor 44, a corresponding respective temperature (T1, T2, ..., Tn) is also applied to the sensor. Preferably, but not necessarily, the pressures and temperatures in theinput 48 span or cover the range of pressures and temperatures over which thesubject sensor 44 is designed to operate in actual practice. - A known accurate
reference pressure sensor 50 which generates anoutput 52 having a known mathematical relationship to aninput 54 thereto including the same pressures (P1, P2, ..., Pn) applied to thesubject sensor 44 may be used in themethod 42 in the same manner as thereference sensor 30 is used in themethod 26 described above. Similarly, a known accuratereference temperature sensor 56 may be used in themethod 42 to generate anoutput 58 in response to aninput 60 including the same temperatures (T1, T2, ..., Tn) applied to thesubject sensor 44, with the output having a known mathematical relationship to the input. However, as described above for thereference sensor 30, if the pressures and/or temperatures in theinput 48 applied to thesubject sensor 44 may be otherwise known, then the pressure and/ortemperature reference sensors temperature inputs method 42 below. - The
subject sensor output 46 is input to aneural network 62 in order to train the neural network. For correspondence with the individual temperatures applied to thesubject sensor 44 to generate theoutput 46, the temperaturereference sensor output 58 is also input to theneural network 62. Theneural network 62 may be, but is not necessarily, of the same type as theneural network 38 described above, except that theneural network 62 is a two input, one output type of neural network. Theneural network 62 is trained until itsoutput 64 in response to input thereto of thesubject sensor output 46 and the temperaturereference sensor output 58 compares with sufficient accuracy to the pressurereference sensor output 52. In this manner, theneural network 62, once trained, generates a calibrated output in response to input thereto ofoutput 46 of thesubject sensor 44 andoutput 58 of thetemperature reference sensor 56, in that theneural network output 64 simulates theoutput 52 of thepressure reference sensor 50. - In actual practice, output of the
subject sensor 44, as well as the actual temperature applied to the subject sensor at the time its output is generated, are input to theneural network 62. Theneural network 62 then generates a calibrated output which compensates for the temperature of the sensor at the time its output was generated. Thesubject sensor 44 and/or theneural network 62 may be included in thetransducer 12 or they may be separately positioned, theneural network 62 may take any form, and the subject sensor and neural network may be directly connected or remotely communicated, as described above for themethod 26. - It will be readily appreciated that the
method 42 permits accurate calibration of a sensor, even though the sensor output may vary in response to a stimulus other than that stimulus for which the sensor output is primarily designed to indicate or represent. In order to generate the calibrated output of the sensor, the neural network has input thereto not only the sensor output, but also the value of the other stimulus which influences the sensor output. For example, if thesubject sensor 44 is a pressure sensor and is included in thetransducer 12 in themethod 10 described above, the known temperature of the sensor at the time it generates its output is used by theneural network 62 to generate the calibrated output which compensates for that temperature. - However, it is sometimes difficult to determine with precision the temperature of a sensor at the time it generates its output. For example, the temperature of the
transducer 12 in themethod 10 at the time of the well test may not be accurately known. For this reason, it is common practice to include a temperature sensor along with a pressure sensor in a transducer used in well tests such as those described above for themethod 10. In that case, the output of the temperature sensor must also be accurately calibrated, so that the output of the pressure sensor may be accurately compensated for temperature applied to the pressure sensor. - Referring additionally now to FIG. 4, another
method 66 of calibrating asensor 68 is schematically and representatively illustrated in flow chart form. Thesubject sensor 68 may be incorporated into thetransducer 12 of themethod 10, or it may be utilized in other methods, other transducers, other applications, etc., without departing from the principles of the present invention. Additionally, thesubject sensor 68 is described herein as being a pressure sensor, i.e., a sensor which produces an output indicative of pressure applied thereto. However, it is to be clearly understood that thesubject sensor 68 may be any type of sensor and may produce an output indicative of stimuli other than pressure in keeping with the principles of the present invention. - The
method 66 also accomplishes calibration of a secondsubject sensor 70 which may also be incorporated into thetransducer 12 of themethod 10, or which may be utilized in other methods, other transducers, other applications, etc. Thesensor 70 is described herein as being a temperature sensor, i.e., a sensor which produces an output indicative of temperature applied thereto. However, it is to be clearly understood that thesubject sensor 70 may be any type of sensor and may produce an output indicative of stimuli other than temperature in keeping with the principles of the present invention. - The
subject temperature sensor 70 is used in themethod 66 to demonstrate how the method may be utilized to advantage in those situations in which thesubject pressure sensor 68 produces an output which is influenced by temperature applied to the subject pressure sensor. Preferably, in these situations, thesubject temperature sensor 70 is positioned in close proximity to thesubject pressure sensor 68, for example, by including both the temperature sensor and the pressure sensor in a single transducer, such as thetransducer 12 in themethod 10, so that the same temperature applied to the pressure sensor is also applied to the temperature sensor. However, it is to be clearly understood that it is not necessary, in keeping with the principles of the present invention, for thesubject sensors - As with the
pressure sensor 44 described above, thesubject pressure sensor 68 generates an output which is indicative of pressure applied thereto, but this output is also influenced, at least in part, by temperature applied to the sensor. This is often the case with sensors which include quartz piezoelectric crystals, and which are frequently used in downhole applications, such as in the types of well tests described above. - In the
method 66, aninput 72 to thesubject pressure sensor 68 includes both pressures and temperatures. Thus, for each pressure (P1, P2, ..., Pn) applied to thesubject pressure sensor 68, a corresponding respective temperature (T1, T2, ..., Tn) is also applied to the sensor. Preferably, but not necessarily, the pressures and temperatures in theinput 72 span or cover the range of pressures and temperatures over which thesubject pressure sensor 68 is designed to operate in actual practice. - A known accurate
reference pressure sensor 74 which generates anoutput 76 having a known mathematical relationship to aninput 78 thereto including the same pressures (P1, P2, ..., Pn) applied to thesubject pressure sensor 68 may be used in themethod 66 in the same manner as thereference sensor 30 is used in themethod 26 described above. Similarly, a known accuratereference temperature sensor 80 may be used in themethod 66 to generate anoutput 82 in response to aninput 84 including the same temperatures (T1, T2, ..., Tn) applied to thesubject pressure sensor 68, with the output having a known mathematical relationship to the input. However, as described above for thereference sensor 30, if the pressures and/or temperatures in theinput 72 applied to thesubject sensor 68 may be otherwise known, then the pressure and/ortemperature reference sensors pressure input 78 andtemperature input 84 may be substituted for the reference sensor outputs 76, 82, respectively, in the further description of themethod 66 below. - The same temperatures (T1, T2, ..., Tn) applied to the
subject pressure sensor 68 in theinput 72 and applied to thetemperature reference sensor 80 in theinput 84 are also applied asinput 86 to thesubject temperature sensor 70. In response, thesubject temperature sensor 70 produces anoutput 88 which is indicative of the temperatures applied to both of thesubject sensors subject pressure sensor 68 produces anoutput 90 which is indicative of the pressures applied thereto, but which is also influenced by the temperatures applied to thesubject sensors - The subject sensor outputs 88, 90 are input to a
neural network 92 in order to train the neural network. Theneural network 92 may be, but is not necessarily, of the same type as theneural network 38 described above, except that theneural network 92 is a two input, two output type of neural network. Theneural network 92 is trained until a pressureindicative output 94 thereof compares with sufficient accuracy to the pressurereference sensor output 76, and a temperatureindicative output 96 thereof compares with sufficient accuracy to the temperaturereference sensor output 82. In this manner, theneural network 92, once trained, generates the calibratedoutputs output 90 of thesubject pressure sensor 68 and theoutput 88 of thesubject temperature sensor 70, in that the neuralnetwork pressure output 94 simulates theoutput 76 of thepressure reference sensor 74 and the neuralnetwork temperature output 96 simulates theoutput 82 of thetemperature reference sensor 80. - In actual practice, output of the
subject pressure sensor 68 and output of thesubject temperature sensor 70 are both input to theneural network 92. Theneural network 92 then generates a calibrated pressure indicative output which compensates for the temperature of thesubject pressure sensor 68 at the time its output was generated, and also generates a calibrated temperature indicative output. Thesubject sensors neural network 92 may be included in thetransducer 12 or they may be separately positioned, theneural network 92 may take any form, and the subject sensors and neural network may be directly connected or remotely communicated, as described above for themethod 26. - It will be readily appreciated that the
method 66 permits accurate calibration of multiple sensors, even though one sensor output may vary in response to a stimulus indicated by the other sensor, which stimulus is other than that stimulus for which the first sensor output is primarily designed to indicate or represent. The neural network has input thereto not only the first sensor output, but also the second sensor output, and in response generates calibrated outputs of both sensors. For example, if thesubject pressure sensor 68 and thesubject temperature sensor 70 are included in thetransducer 12 in themethod 10 described above, the temperature of the pressure sensor at the time it generates its output, as indicated by the temperature sensor, is used by theneural network 92 to generate a calibrated pressure output which compensates for that temperature, and to generate a calibrated temperature output. Of course, theneural network 92 may only generate one of the outputs, if desired, without departing from the principles of the present invention. - Unfortunately, in some cases, a temperature sensor is also exposed to pressures applied to a pressure sensor, and the output of the temperature sensor is influenced by those pressures. This is frequently the case where a quartz piezoelectric crystal is included in the temperature sensor. In these situations, the temperature sensor output may be compensated for the pressures applied thereto in a similar manner to that in which the pressure sensor output is compensated for the temperatures applied thereto.
- Referring additionally now to FIG. 5, another
method 98 of calibrating asensor 100 is schematically and representatively illustrated in flow chart form. Thesubject sensor 100 may be incorporated into thetransducer 12 of themethod 10, or it may be utilized in other methods, other transducers, other applications, etc., without departing from the principles of the present invention. Additionally, thesubject sensor 100 is described herein as being a pressure sensor, i.e., a sensor which produces an output indicative of pressure applied thereto. However, it is to be clearly understood that thesubject sensor 100 may be any type of sensor and may produce an output indicative of stimuli other than pressure in keeping with the principles of the present invention. - The
method 98 also accomplishes calibration of asecond sensor 102 which may also be incorporated into thetransducer 12 of themethod 10, or which may be utilized in other methods, other transducers, other applications, etc. Thesensor 102 is described herein as being a temperature sensor, i.e., a sensor which produces an output indicative of temperature applied thereto. However, it is to be clearly understood that thesubject sensor 102 may be any type of sensor and may produce an output indicative of stimuli other than temperature in keeping with the principles of the present invention. - The
subject temperature sensor 102 is used in themethod 98 to demonstrate how the method may be utilized to advantage in those situations in which thesubject pressure sensor 100 produces an output which is influenced by temperature applied to the subject pressure sensor, and in which the subject temperature sensor produces an output which is influenced by pressure applied to the subject temperature sensor. Preferably, in these situations, thesubject temperature sensor 102 is positioned in close proximity to thesubject pressure sensor 100, for example, by including both the temperature sensor and the pressure sensor in a single transducer, such as thetransducer 12 in themethod 10, so that the same temperature and pressure applied to the pressure sensor are also applied to the temperature sensor. However, it is to be clearly understood that it is not necessary, in keeping with the principles of the present invention, for thesubject sensors - As with the
pressure sensor 44 described above, thesubject pressure sensor 100 generates an output which is indicative of pressure applied thereto, but this output is also influenced, at least in part, by temperature applied to the sensor. Conversely, thesubject temperature sensor 102 generates an output which is indicative of temperature applied thereto, but this output is also influenced, at least in part, by pressure applied to the sensor. This is often the case with sensors which include quartz piezoelectric crystals, and which are frequently used in downhole applications, such as in the types of well tests described above. - In the
method 98, an input 104 to thesubject pressure sensor 100 includes both pressures and temperatures. Thus, for each pressure (P1, P2, ..., Pn) applied to thesubject pressure sensor 100, a corresponding respective temperature (T1, T2, ..., Tn) is also applied to the sensor. Preferably, but not necessarily, the pressures and temperatures in the input 104 span or cover the range of pressures and temperatures over which thesubject pressure sensor 100 is designed to operate in actual practice. - A known accurate
reference pressure sensor 106 which generates anoutput 108 having a known mathematical relationship to aninput 110 thereto including the same pressures (P1, P2, ..., Pn) applied to thesubject pressure sensor 100 may be used in themethod 98 in the same manner as thereference sensor 30 is used in themethod 26 described above. Similarly, a known accuratereference temperature sensor 112 may be used in themethod 98 to generate anoutput 114 in response to aninput 116 including the same temperatures (T1, T2, ..., Tn) applied to thesubject pressure sensor 100, with the output having a known mathematical relationship to the input. However, as described above for thereference sensor 30, if the pressures and/or temperatures in the input 104 applied to thesubject sensor 100 may be otherwise known, then the pressure and/ortemperature reference sensors pressure input 110 andtemperature input 116 may be substituted for the reference sensor outputs 108, 114, respectively, in the further description of themethod 98 below. - The same temperatures (T1, T2, ..., Tn) and pressures (P1, P2, ..., Pn) applied to the
subject pressure sensor 100 in the input 104 and applied to thereference sensors inputs input 118 to thesubject temperature sensor 102. Thus, theinput 118 is the same as input 104. In response, thesubject temperature sensor 102 produces anoutput 120 which is indicative of the temperatures applied to both of thesubject sensors subject pressure sensor 100 produces anoutput 122 which is indicative of the pressures applied thereto, but which is also influenced by the temperatures applied to thesubject sensors - The subject sensor outputs 120, 122 are input to a
neural network 124 in order to train the neural network. Theneural network 124 may be, but is not necessarily, of the same type as theneural network 38 described above, except that theneural network 124 is a two input, two output type of neural network. Theneural network 124 is trained until a pressureindicative output 126 thereof compares with sufficient accuracy to the pressurereference sensor output 108, and a temperatureindicative output 128 thereof compares with sufficient accuracy to the temperaturereference sensor output 114. In this manner, theneural network 124, once trained, generates the calibratedoutputs output 122 of thesubject pressure sensor 100 and theoutput 120 of thesubject temperature sensor 102, in that the neuralnetwork pressure output 126 simulates theoutput 108 of thepressure reference sensor 106 and the neuralnetwork temperature output 128 simulates theoutput 114 of thetemperature reference sensor 112. - In actual practice, output of the
subject pressure sensor 100 and output of thesubject temperature sensor 102 are both input to theneural network 124. Theneural network 124 then generates a calibrated pressure indicative output which compensates for the temperature of thesubject pressure sensor 100 at the time its output was generated, and also generates a calibrated temperature indicative output which compensates for the pressure applied to thesubject temperature sensor 102 at the time its output was generated. Thesubject sensors neural network 124 may be included in thetransducer 12 or they may be separately positioned, theneural network 124 may take any form, and the subject sensors and neural network may be directly connected or remotely communicated, as described above for themethod 26. - It will be readily appreciated that the
method 98 permits accurate calibration of multiple sensors, even though each sensor output may vary in response to a stimulus indicated by another sensor, which stimulus is other than that stimulus for which each sensor output is primarily designed to indicate or represent. The neural network has input thereto not only the first sensor output, but also the second sensor output, and in response generates calibrated outputs of both sensors. For example, if thesubject pressure sensor 100 and thesubject temperature sensor 102 are included in thetransducer 12 in themethod 10 described above, the temperature of the pressure sensor at the time it generates its output, as indicated by the temperature sensor, is used by theneural network 124 to generate a calibrated pressure output which compensates for that temperature, and the pressure applied to the temperature sensor at the time it generates its output, as indicated by the pressure sensor, is used by theneural network 124 to generate a calibrated temperature output which compensates for that pressure. Note that theneural network 124 may only generate one of the outputs, without departing from the principles of the present invention. - Unfortunately, in some cases, the output of a pressure sensor is not only influenced by the temperature of the sensor at the time its output is generated, but is also influenced by changes in its temperature. This is frequently the case where a quartz piezoelectric crystal is included in the pressure sensor. The pressure sensor output may also, or alternatively, be influenced by other factors, such as by changes in the pressure applied to the sensor. In these situations, the pressure sensor output would desirably be compensated for changes in the stimulus applied thereto. These stimulus changes may be a first order, or higher order, derivative or integral of the level of the stimulus over the time the stimulus is applied to the sensor.
- Referring additionally now to FIG. 6, another
method 130 of calibrating asensor 132 is schematically and representatively illustrated in flow chart form. Thesubject sensor 132 may be incorporated into thetransducer 12 of themethod 10, or it may be utilized in other methods, other transducers, other applications, etc., without departing from the principles of the present invention. Additionally, thesubject sensor 132 is described herein as being a pressure sensor, i.e., a sensor which produces an output indicative of pressure applied thereto. However, it is to be clearly understood that thesubject sensor 132 may be any type of sensor and may produce an output indicative of stimuli other than pressure in keeping with the principles of the present invention. - The
method 130 may also accomplish calibration of asecond sensor 134 which may also be incorporated into thetransducer 12 of themethod 10, or which may be utilized in other methods, other transducers, other applications, etc. Thesubject temperature sensor 134 is shown in dashed lines in FIG. 6 to indicate that it may or may not be included in themethod 130. For example, where the output of thesubject pressure sensor 132 is influenced by its temperature and changes in that temperature, and those temperatures and changes in temperature may be known without the use of a temperature sensor, then use of thesubject temperature sensor 134 is unnecessary. However, preferably a temperature sensor positioned in close proximity to thesubject pressure sensor 132 is utilized in order to provide indications of the actual temperatures and changes in temperature experienced by the pressure sensor. - The
sensor 134 is described herein as being a temperature sensor, i.e., a sensor which produces an output indicative of temperature applied thereto. However, it is to be clearly understood that thesubject sensor 134 may be any type of sensor and may produce an output indicative of stimuli other than temperature in keeping with the principles of the present invention. - The
subject temperature sensor 134 is used in themethod 130 to demonstrate how the method may be utilized to advantage in those situations in which thesubject pressure sensor 132 produces an output which is influenced by temperatures and changes in temperature applied to the subject pressure sensor. Note that thesubject temperature sensor 134 may produce an output which is influenced by pressures and changes in pressure applied to the subject temperature sensor. Preferably, in these situations, thesubject temperature sensor 134 is positioned in close proximity to thesubject pressure sensor 132, for example, by including both the temperature sensor and the pressure sensor in a single transducer, such as thetransducer 12 in themethod 10, so that the same temperatures and pressures applied to the pressure sensor are also applied to the temperature sensor. However, it is to be clearly understood that it is not necessary, in keeping with the principles of the present invention, for thesubject sensors - As with the
pressure sensor 44 described above, thesubject pressure sensor 132 generates an output which is indicative of pressure applied thereto, but this output may also be influenced, at least in part, by temperature applied to the sensor, by changes in temperature applied to the sensor, or by changes in the pressure applied to the sensor. Conversely, thesubject temperature sensor 134 generates an output which is indicative of temperature applied thereto, but this output may also be influenced, at least in part, by pressure applied to the sensor, by changes in pressure applied to the sensor, or by changes in temperature applied to the sensor. This may be the case with sensors which include quartz piezoelectric crystals, and which are frequently used in downhole applications, such as in the types of well tests described above. - In the
method 130, aninput 136 to thesubject pressure sensor 132 may include both pressures and temperatures applied over time. Thus, for each pressure (P1, P2, ..., Pn) applied to thesubject pressure sensor 132, a corresponding respective temperature (T1, T2, ..., Tn) may also be applied to the sensor. Preferably, but not necessarily, the pressures and temperatures in theinput 136 span or cover the range of pressures and temperatures over which thesubject pressure sensor 132 is designed to operate in actual practice. - A known accurate
reference pressure sensor 138 which generates anoutput 140 having a known mathematical relationship to aninput 142 thereto including the same pressures (P1, P2, ..., Pn) applied to thesubject pressure sensor 132 may be used in themethod 130 in the same manner as thereference sensor 30 is used in themethod 26 described above. Similarly, a known accuratereference temperature sensor 144 may be used in themethod 130 to generate anoutput 146 in response to aninput 148 including the same temperatures (T1, T2, ..., Tn) applied to thesubject pressure sensor 132, with the output having a known mathematical relationship to the input. However, as described above for thereference sensor 30, if the pressures and/or temperatures in theinput 136 applied to thesubject sensor 132 may be otherwise known, then the pressure and/ortemperature reference sensors pressure input 142 andtemperature input 148 may be substituted for the reference sensor outputs 140, 146, respectively, in the further description of themethod 130 below. - The same temperatures (T1, T2, ..., Tn) and pressures (P1, P2, ..., Pn) applied to the
subject pressure sensor 132 in theinput 136 and applied to thereference sensors inputs input 150 to thesubject temperature sensor 134. Thus, theinput 150 is the same asinput 136 for those cases where thesubject temperature sensor 134 is used and the subject temperature sensor has an output which is influenced by pressure applied thereto. Of course, if thesubject pressure sensor 132 output is unaffected by temperature and/or changes in temperature, then there is no need for its input to include the temperatures (T1, T2, ..., Tn) and there is no need for thesubject temperature sensor 134 to be included in themethod 130. If thesubject temperature sensor 134 is used in themethod 130, but its output is unaffected by pressures and/or changes in pressure applied thereto, then there is no need for its input to include the pressures (P1, P2, ..., Pn). - In response to the
input 150, thesubject temperature sensor 134 produces anoutput 152 which is indicative of the temperatures applied to both of thesubject sensors subject pressure sensor 132 produces anoutput 154 which is indicative of the pressures applied thereto, but which may also be influenced by the temperatures and/or changes in temperature and/or pressure applied to thesubject sensors - A
clock 158 is provided in themethod 130, so that the relative time at which each of the pressures (P1, P2, ..., Pn) and/or temperatures (T1, T2, ..., Tn) is/are applied to the subject pressure and/ortemperature sensors clock 158 produces anoutput 160 indicative of the time at which corresponding respective pressures and/or temperatures are applied in theinputs - The subject sensor outputs 152, 154 and
clock output 160 are input to aneural network 156 in order to train the neural network. Theneural network 156 may be, but is not necessarily, of the same type as theneural network 38 described above, except that theneural network 156 may be either a two input, one output type of neural network, or a three input, two output type of neural network, depending upon whether data indicative of multiple stimuli is desired to be input to the neural network. Theneural network 156 is trained until a pressureindicative output 162 thereof compares with sufficient accuracy to the pressurereference sensor output 140, and a temperatureindicative output 164 thereof, if desired, compares with sufficient accuracy to the temperaturereference sensor output 146. In this manner, theneural network 156, once trained, generates the calibratedoutputs 162 and/or 164 in response to input thereto of theclock output 160 and theoutput 154 of thesubject pressure sensor 132 and/or theoutput 152 of thesubject temperature sensor 134, in that the neuralnetwork pressure output 162 simulates theoutput 140 of thepressure reference sensor 138 and the neuralnetwork temperature output 164, if generated, simulates theoutput 146 of thetemperature reference sensor 144. - In actual practice, output of the
subject pressure sensor 132 and output of thesubject temperature sensor 134, if used, are input to theneural network 156, along with theclock output 160. Theneural network 156 may then generate a calibrated pressure indicative output which compensates for the temperature and changes in temperature of thesubject pressure sensor 132 and/or changes in pressure at the time its output was generated, and may also generate a calibrated temperature indicative output which compensates for the pressure and/or changes in pressure applied to thesubject temperature sensor 134 and/or changes in temperature at the time its output was generated. Thesubject sensors clock 158 and/or theneural network 156 may be included in thetransducer 12 or they may be separately positioned, theneural network 156 may take any form, and the subject sensors and neural network may be directly connected or remotely communicated, as described above for themethod 26. - Note that, the
clock 158 output may also be affected by stimulus applied thereto. For example, if theclock 158 is included in thetransducer 12 in themethod 10, it may also be subjected to temperatures the same as, or similar to, those experienced by one or more sensors in the transducer. If desired, the principles of the present invention may be utilized to compensate for such stimulus and /or changes in stimulus applied to theclock 158 in a manner similar to that described above for compensating for stimulus and/or changes in stimulus applied to sensors. For example, a reference clock (not shown in FIG. 6) may be used in themethod 130 to generate an output indicative of actual relative time, while theclock 158 is subjected to thetemperature input 148. Of course, in actual practice it is not necessary for theclock 158 to be subjected to any stimulus also experienced by sensors, since the clock could be at the earth's surface or otherwise remotely located with respect to the sensors, or the clock may be otherwise isolated from one or more stimuli experienced by the sensors. - It will be readily appreciated that the
method 130 permits accurate calibration of one or more sensors, even though a sensor output may vary in response to a stimulus or change in stimulus indicated by the sensor, or by a stimulus or change in stimulus indicated by another sensor. Theneural network 156 has input thereto not only the one or more sensor output(s), but also relative times at which the output(s) were generated, and in response generates calibrated output(s) of the sensor(s). For example, if thesubject pressure sensor 132 and thesubject temperature sensor 134 are included in thetransducer 12 in themethod 10 described above, the temperature of the pressure sensor and the change in temperature at the time it generates its output, as indicated by the temperature sensor and the clock, are used by theneural network 156 to generate a calibrated pressure output which compensates for that temperature and change in temperature, and the pressure applied to the temperature sensor and the change in pressure at the time it generates its output, as indicated by the pressure sensor and the clock, are used by theneural network 156 to generate a calibrated temperature output which compensates for that pressure and change in pressure. Note that theneural network 156 may only generate one of the outputs, without departing from the principles of the present invention. - Referring additionally now to FIG. 7, a
method 166 of generating change-compensated calibrated outputs of one or more sensors is representatively and schematically illustrated in flow chart form. In the following description of themethod 166, theneural network 156 anduncalibrated outputs pressure sensors method 166 may be utilized advantageously. However, it is to be clearly understood that themethod 166 may be used with other types of data input, other numbers of sensor outputs, other types of sensor outputs, other inputs, other neural networks, etc., without departing from the principles of the present invention. Thus, themethod 166 is not to be considered as limited to the specific embodiment thereof described herein. - In the
method 166, thepressure sensor output 154,temperature sensor output 152 andclock output 160 are input to theneural network 156. For clarity of description,pressure sensor data 168 input to theneural network 156, which data includes thepressure sensor output 154, is represented in FIG. 7 as a series of pressure indications (P(n+M), ..., P(n), ..., P(n-N)) separated by time delays (D). Similarly,temperature sensor data 170 input to theneural network 156, which data includes thetemperature sensor output 152, is represented in FIG. 7 as a series of temperature indications (T(n+M), ..., T(n), ..., T(n-N)) separated by time delays (D). It will be readily appreciated that the time delays (D) are derived from theclock output 160. Although the time delays (D) between each pair of pressure and temperature indications are shown in FIG. 7 as being equal, such is not necessary in themethod 166. - The pressure indication and corresponding temperature indication input to the
neural network 156, for which a current calibrated output of each from the neural network is desired, are designated as P(n) and T(n), respectively, in FIG. 7. The calibratedoutputs method 166 are designated Pcal(n) and Tcal(n), respectively, in FIG. 7. - Note that the
pressure input data 168 includes not only the pressure indication P(n), but also pressure indications prior to, and subsequent to, the pressure indication P(n). Similarly, thetemperature input data 170 includes not only the temperature indication T(n), but also temperature indications prior to, and subsequent to, the temperature indication T(n). The pressure indications prior to P(n) are designated P(n-N), P(n-N+1), ..., with N representing the number of prior pressure indications input to the neural network, and the pressure indications subsequent to P(n) are designated P(n+M), P(n+M-1), ..., with M representing the number of subsequent pressure indications input to theneural network 156. Similarly, the temperature indications prior to T(n) are designated T(n-N), T(n-N+1), ..., with N representing the number of prior temperature indications input to the neural network, and the temperature indications subsequent to T(n) are designated T(n+M), T(n+M-1), ..., with M representing the number of subsequent temperature indications input to theneural network 156. - Note also that, although these pressure and temperature designations are depicted in FIG. 7 and described above as representing respective discrete pressure and temperature indications between corresponding pairs of the delays (D), it is to be clearly understood that these designations preferably represent averages of respective pressure and temperature indications over each corresponding time delay (D). Thus, P(n) may be an average of multiple pressure indications in the
pressure sensor output 154, and T(n) may be an average of multiple temperature indications in thetemperature sensor output 152. - The
neural network 156 is trained to produce pressure and temperature indicative outputs in response to thepressure sensor data 168, and thetemperature sensor data 170, until theoutputs neural network 156, the neural network will output accurate calibrated pressure and temperature indications. Thismethod 166 as described above, wherein prior and subsequent pressure and temperature indications are input to theneural network 156, results in significant "smoothing" of the pressure and temperature curves produced by the calibrated pressure andtemperature outputs - In a further refinement of the
method 166, additional inputs to theneural network 156 may include those produced by tappeddelay lines pressure output 172 may be tapped by thedelay line 176, so that prior calibrated pressure outputs (designated in FIG. 7 as Pcal(n-Q), Pcal(n-Q+1), ..., Pcal(n-1), where Q represents the number of prior calibrated pressure outputs tapped) may be input back into theneural network 156. Similarly, the calibratedtemperature output 174 may be tapped by thedelay line 178, so that prior calibrated pressure outputs (designated in FIG. 7 as Tcal(n-Q), Tcal(n-Q+1), ..., Tcal(n-1)) may be input back into theneural network 156. - FIGS. 8 & 9 demonstrate the substantial increase in accuracy of sensor outputs which may be achieved using the methods described herein. FIG. 8 shows actual pressure and temperature outputs of respective pressure and temperature sensors. The pressure sensor was subjected to a relatively constant pressure of about 94 psi (648 kPa) during the test represented in FIG. 8. However, the pressure sensor was of the type which has an output influenced by changes in temperature. Note that, at about 225 seconds into the test, an increase in temperature of about 50° F (10°C) in the environment surrounding the pressure sensor produced an indicated drop in pressure of about 45 psi (310 kPa), even though the pressure applied to the pressure sensor actually remained relatively constant. At about 2200 seconds into the test a decrease in temperature was seen to produce an indicated increase in pressure when, again, the actual pressure remained relatively constant.
- In FIG. 9, the results of use of the methods described herein may be clearly seen. The same pressure and temperature data which produced the curves shown in FIG. 8 were input to a neural network as described above for the
method 166, wherein 70 prior pressure and temperature indications (N=70) and 30 subsequent pressure and temperature indications (M=30) were used, along with a tapped delay line from the resulting output of each. Although the pressure curve shown in FIG. 9 does still include some minor indications of the thermal transients applied to the pressure sensor in this test, it will be readily appreciated that the present invention provides a substantial improvement over static calibration methods used in the past and, indeed, provides dynamic calibration. The calibration is dynamic in that changes in stimulus applied to a sensor, which changes influence the sensor output, may be compensated for by utilizing a neural network trained to recognize such changes and calibrate the sensor therefor. - Of course, upon a careful consideration of the specific embodiments of the present invention described above, a person skilled in the art will readily appreciate that certain modifications, substitutions, additions, deletions and other changes may be made to these embodiments without substantively deviating from the principles of the present invention.
Claims (10)
- A calibration method comprising the steps of: applying an input to a first subject sensor, the first subject sensor input including a series of levels of a first stimulus; generating an output of the first subject sensor in response to the first subject sensor input, the first subject sensor output including a series of uncalibrated measurements of corresponding respective ones of the series of first stimulus levels; inputting the first subject sensor output to a neural network; and training the neural network to generate a calibrated output of the first subject sensor.
- A method according to Claim 1, further comprising the steps of: applying an input to a second subject sensor, the second subject sensor input including a series of levels of a second stimulus; generating an output of the second subject sensor in response to the second subject sensor input, the second subject sensor output including a series of uncalibrated measurements of corresponding respective ones of the series of second stimulus levels; and inputting the second subject sensor output to the neural network, and wherein the training step further comprises training the neural network to generate a calibrated output of the second subject sensor.
- A method according to Claim 1 or 2, wherein in the training step, the neural network generates a first output including a series of measurements indicative of corresponding respective ones of the series of first stimulus levels.
- A method of calibrating first and second sensors, the first sensor generating an output indicative of a first series of levels of a first stimulus applied to the first sensor and influenced by a change in a second series of levels of a second stimulus applied to the first and second sensors, and the second sensor generating an output indicative of the second series of levels of the second stimulus, the method comprising the steps of: time indexing the first and second sensor outputs; inputting the first and second sensor outputs to a neural network; and training the neural network by generating a first output of the neural network corresponding to the first sensor output, utilizing a first tapped delay line to input a first portion of the neural network first output to the neural network, generating a second output of the neural network corresponding to the second sensor output, and utilizing a second tapped delay line to input a second portion of the neural network second output to the neural network.
- A method according to Claim 4, wherein the first sensor output includes a series of first uncalibrated measurements corresponding to respective ones of the first series of the levels of the first stimulus, and wherein in the training step, for each one of a series of first measurements included in the first neural network output corresponding to a respective one of the first series of uncalibrated measurements, a first predetermined quantity of the series of the first uncalibrated measurements prior to the respective one of the first series of uncalibrated measurements is input to the neural network.
- A method of calibrating a first sensor operatively positionable in a subterranean well, the method comprising the steps of: applying a first sensor input to the first sensor, the first sensor input including multiple levels of a first stimulus; generating a first output of the first sensor in response to the first sensor input; inputting the first sensor first output to a neural network; and training the neural network so that the neural network generates a first neural network output which is related to the first sensor input by a first known mathematical function.
- A method according to Claim 6, further comprising the steps oft applying a second sensor input to a second sensor, the second sensor input including multiple levels of a second stimulus; and generating a first output of the second sensor in response to the second sensor input, and wherein the inputting step further comprises inputting the second sensor first output to the neural network, and wherein the training step further comprises training the neural network so that the neural network generates a second neural network output which is related to the second sensor input by a second known mathematical function.
- Apparatus operative in conjunction with a subterranean well, the apparatus comprising: a first sensor generating an output indicative of a series of first stimulus levels applied to the first sensor, the first sensor output including a series of first uncalibrated measurements of corresponding respective ones of the series of first stimulus levels; and a neural network generating an output in response to the first sensor output, the neural network output including a series of first calibrated measurements of corresponding respective ones of the series of first stimulus levels.
- Apparatus according to Claim 8, further comprising a second sensor generating an output indicative of a series of second stimulus levels applied to the second sensor, the second sensor output including a series of second measurements of corresponding respective ones of the series of second stimulus levels, wherein the first sensor output is influenced at least in part by the series of second stimulus levels, and wherein the neural network output is generated further in response to the second sensor output.
- Apparatus according to Claim 9, wherein a portion of the neural network output is input to the neural network.
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US298691 | 1981-09-02 | ||
US09/298,691 US6594602B1 (en) | 1999-04-23 | 1999-04-23 | Methods of calibrating pressure and temperature transducers and associated apparatus |
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EP1046885A1 true EP1046885A1 (en) | 2000-10-25 |
EP1046885B1 EP1046885B1 (en) | 2009-07-29 |
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CN113916329A (en) * | 2021-11-03 | 2022-01-11 | 国家石油天然气管网集团有限公司 | Natural gas flowmeter calibrating device and method based on neural network |
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US6594602B1 (en) | 2003-07-15 |
DE60042627D1 (en) | 2009-09-10 |
EP1046885B1 (en) | 2009-07-29 |
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